The two-point function that we would like to compare is determined by the renormalised geodesic distance \(d\)  of two boundary points in the shockwave geometry,
 
ML(tL)MR(tR)e-mprobe d,

where \(m_{\rm probe}\)  is the mass of a probe particle.
Since JT gravity is an s-wave reduction of the three-dimensional Einstein gravity [1]}, we can use the result from [2]}, which is

e-mprobe d=((TBH(tR-tL))+shock2e-TBH(tR+tL))-2mprobeAdS.

where the operators are inserted at times \({\tilde{t}}_{L,R}\)  on the two sides, and \(T_{BH}=R_{BH}/2\pi l_{AdS}^2 \) . \(\alpha _{\text{shock}}\)  quantifies the strength of the shock and is given by \(\alpha _{\text{shock}}=(E/M_{BH}) e^{2\pi T_{BH}{\tilde{t}}_w}\)  where \({\tilde{t}}_w\)  is the time of shock and we take it to infinity as we take \(E/M_{BH}\rightarrow 0\)  keeping \(\alpha _{\text{shock}}\)  fixedThe computation was done in the theory of three-dimensional gravity, but since they considered the shockwave to be S-wave, we can do the dimensional reduction and then the result is the same as in JT gravity..
By Fourier transforming in terms of \(\tilde{t}_{L,R}\) , this can be rewritten as
\(e^{-m_{\rm probe}d}=\frac{1}{(2\pi T_{\rm BH})^2}&\int \frac{d\tilde{\omega }_L}{2\pi }\,\frac{d\tilde{\omega }_R}{2\pi }\,e^{-i\tilde{t}_L\tilde{\omega }_L-i\tilde{t}_R\tilde{\omega }_R}\left(\alpha _{\rm shockwave}\right)^{-\frac{i(\tilde{\omega }_L+\tilde{\omega }_R)}{2\pi T_{\rm BH}}}\\&\quad \times \frac{\Gamma \left(m_{\rm probe}\ell _{\rm AdS}-\frac{i\tilde{\omega }_L}{2\pi T_{\rm BH}}\right)\Gamma \left(m_{\rm probe}\ell _{\rm AdS}-\frac{i\tilde{\omega }_R}{2\pi T_{\rm BH}}\right)\Gamma \left(\frac{i(\tilde{\omega }_L+\tilde{\omega }_R)}{2\pi T_{\rm BH}}\right)}{\Gamma (2m_{\rm probe}\ell _{\rm AdS})}\) 
